(1) How does the graph of #y=3cos(x/2)# compare to the standard graph of #y=cosx#? (2) If #f(x)=k+Acos(B(x-h))# represents the graph of a general cosine function, how do you find #k, A, B and h# in this case?

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Answer 1 · 2017-11-04T03:07:11

See below.

#y=3cos(x/2)#

#1. y# is simply the standard graph of #cosx# scaled by 3 units with a period extended ("stretched") to #4pi#.

It has a zero at #pi# since #cos(pi/2)=0#

N.B. A similar sine curve would have a value of 0 at #x=0#

#2#. Equating #y# to #k+Acos(B(x-h))#

#-> k=h=0, A=3, B=1/2#